Physics 2112

Unit 12

Today’s Concept:

Magnetic Force on Moving Charges

Unit 12, Slide 1

F=qv x B

Where we are……

E fields

B fields

This is crazy. But also really cool.What is that "K" = p^2/2m? i saw it in the prelecture question but ididnt see it in the actual prelecture slide.Need to go over Question 3 in Pre-Lecture. If R=mv/qB then wouldn't a particle with 2x the charge and 4x the mass have 2x the R???????The derived equations were difficult for meunits units units.... how well do we have to know prefixes for the upcoming test?Would like to see examples of cross productI got confused comparing the magnitude of the magnetic field at chamber 1 and 2.I need to review cross products & also are we using the vector from the electric field generated by the particle as the 2nd vector? Because that makes more sense.

Stuff You asked about…..

Magnetic Force

Unit 12, Slide 4

Electric Field

• Any particle can cause E field

• Any particle affected by E field

Magnetic Field

• Only moving particle can cause B field

• Only moving particle affected by B field

F=qv x B

Units

Unit 12, Slide 5

• Earth ~ 0.6 Gauss

• Frig Magnet ~ 0.01T (100 Gauss)

• MRI 1.5 ->5.0 Tesla (15,000 – 30,000 Gauss)

• LHC 8.4 Tesla

• World’s Record 45.5 Tesla (National High

Magnetic Field Laboratory at Florida State)

Units: Tesla (N/(Cm/sec))

Extremely large field so sometimes

use Gauss = (10-4T)

Cross Product Review

Cross Product different from Dot Product

is a scalar; is a vector

proportional to the component of B parallel to A

proportional to the component of B perpendicular to A

Definition of

Magnitude: |A||B|sinq

Direction: perpendicular to plane defined by A and B with sense given by right-hand-rule

Unit 12, Slide 6

A B

A B

xy

z

BF

qv

Remembering Directions: The Right Hand Rule

Unit 12, Slide 7

F=qv x B

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

A positive particle enters a

magnetic field that points into

the page. The direction of the

particle is shown to the left.

What can I say about the x and

y portions of the resulting force?

A) Fx is positive and Fy is positive

B) Fx is negative and Fy is negative

C) Fx is negative and Fy is postivie

D) Fx is positive and Fy is negative

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

A particle enters a

magnetic field

𝐵 = −0.2𝑘𝑇

The particle had charge

of 1uC and a velocity of

What is the force on the

particle?

sec/)ˆ7.0ˆ3.0( mjiv +−=

A permanent magnet has field lines as shown above. An electron moves out of the slide toward you at point A. The magnetic force on the electron is best represented by:

A

B

C

D

Question

A B

D E

C

A proton moves to the right at point B. The magnetic force on the proton is best represented by:

A B

D E

C

Question

A

B

C

D

A

B

C

DA proton is at rest at point D. The magnetic force on the proton is best represented by:

Question

A B

D E

C

Example 12.1 (Acceleration of proton)

Unit 12, Slide 13

The earth’s magnetic field is pointed

roughly 70o from the horizontal in

Chicago.

What would the acceleration of a

proton be if it were moving at 10% of

the speed of light in the horizontal

direction?

CheckPoint 2

Three points are arranged in a uniform magnetic field. The B field points into the screen.

Unit 12, Slide 14

A positively charged particle is located at point A and is stationary.

The direction of the magnetic force on the particle is:

A. right B. left C. into the screen D. out of the screen E. zero

CheckPoint 3

Three points are arranged in a uniform magnetic field. The B field points into the screen.

Unit 12, Slide 15

Now the positive charge moves from point A toward B.

The direction of the magnetic force on the particle is:

A. right B. left C. into the screen D. out of the screen E. zero

A particle of charge +q and velocity v enters a vacuum containing a uniform magnetic field, B. The particle’s velocity is perpendicular to the direction of the field.

After the particle enters the magnetic field, its path is

A. a parabola.

B. circular.

C. spiral.

D. a straight line

E. a hyperbola

Q

X X X X X X

X X X X X X

X X X X X X

X X X X X X

X X X X X X

X X X X X X

Question

Motion of Charge q in Uniform B Field

x x x x x x x

x x x x x x x

x x x x x x x

x x x x x x x

x x x x x x x

x x x x x x x

Uniform B into page

Force is perpendicular to vSpeed does not change

Uniform Circular Motion

Solve for R:

R

Demo

qvBFBvqF ==

R

va

2

=

R

vmqvB

2

=

q

q q

v

F

v

F

v

F

v

F

q

qB

mvR =

Unit 12, Slide 17

Example 12.2 (Analysis Magnets)

Unit 12, Slide 18

A proton enters the magnetic field of an

analysis magnet at Fermilab and it

deflected by an angle of Q = 10o. The

field has a strength of 0.2T and a

length of 2meters. What is the speed of

the incoming proton?

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

Q

X X X X X X X

X X X X X X X

Q R sinQ

Follow up

Unit 12, Slide 19

The analysis

magnet

Photograph of

track in bubble

chamber (pre

1984)

Electronic

version of

same thing

(top quark

event at CDF)

Question: In the previous example how did

you know it was a proton?

Example 12.3 (Effect of v on R and f)

Unit 12, Slide 20

A proton moving in a circle with a

radius R inside a constant magnetic

field. It completes the circle with some

period, T.

If you double velocity of the particle,

how does the radius change?

How does the period change?

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

What good is this?

Two Copper “D”s

X

X X X X X X

X X X X X X X X

X X X X X X X X X X

X X X X X X X X X X X

X X X X X X X X X X X

X X X X X X X X X X X

X X X X X X X X X X X

X X X X X X X X X X

X X X X X X X X

X X X X X X

X

Circular Magnetic Field

(to steer)

Alternating E Field Btwn “D”

(to increase v)

Accelerated Particles

E.O. Lawrence

1939 Nobel Prize in Physics

for “cyclotron”

LHC

Unit 12, Slide 22

How big are these things?

E=80,000eV

LHC

LHC Swiss-French Border

R = 4.2km

Unit 12, Slide 23

How big are these things?

E=7,000,000,000,000 eV

Example 12.4 (mass spectrometer)

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

Using a velocity selector, singly ionized U235 and U238 atoms are injected in a 0.3T magnetic field at 100m/sec. If they are allowed to travel 180o, how far from will the two isotopes be?

An airplane viewed from above flies through a small magnetic field oriented vertically downward toward the ground, as shown to the right. Which of the following statements is true?

D. None of the above, there’s no charging mechanism.

A. The plane’s front becomes positively charged.

B. The tip of the left wing becomes positively charged.

C. The top of the plane becomes positively charged.

Question

The Hall

Effect